Remark on the energy channel property for the radial linear wave equation

This note concerns an exterior energy bound (channel of energy property) for the linear radial wave equations, which is crucial in the proof of the soliton resolution for the energy-critical wave equations. We give a short and synthetic proof that this property in general odd space dimension follows from the case of space dimension 3, which is elementary. This gives a simple proof of the channel of energy property in all odd space dimensions. We also show by the same proof that the analogous bound in even space dimensions follows from the case of space dimension 4.